The Wigner function for ideal GKP states consists of a linear combination of two-dimensional \(\delta \) -functions in phase space [1]}:
\(\begin{split}W_{\mathinner {|{+}\rangle }_{\rm gkp}}(\mathbf {r}) &= \frac{\sqrt{\pi }}{2}\sum _{s,t=-\infty }^{\infty } (-1)^{st}\delta (\mathbf {r}-\mathbf {\mu }_{s,t}),\\\mathbf {\mu }_{s,t}^T &= \frac{\sqrt{\pi }}{2}(s,2t).\end{split}\) 
